Many attempts have been made to relate happiness with various factors. One such study relates happiness with age and finds that holding everything else constant, people are least happy when they are in their mid-40s (The Economist, December 16, 2010). Consider the following table for data on a respondent’s age and his/her perception of well-being on a scale from 0 to 100. A portion of the data is presented below; the entire data set, labeled Happiness_Age, can be found on the text website.
Age ... Happiness
49 ... 62
51 ... 66
69 ... 72

a. Calculate and interpret the sample correlation coefficient between age and happiness.
b. Construct a scatter plot to point out a law with the above correlation analysis.